RJ45 data jacks have four connection pairs for laying and/or connecting core pairs of a four-pair data cable, each connection pair of the data jack being used for laying and/or connecting a core pair of the data cable. In order to facilitate the connection of the core pairs of the data cable to the connection pairs of the data jack, color coding is assigned to the connection pairs of the data jack, which color coding corresponds to the colored sheathing of the cores of the core pairs of the data cable. The color coding is in this case carried out in accordance with the standard TIA/EIA 568 A or the standard TIA/EIA 568 B. When the core pairs of the data cable are laid on the corresponding connection pairs of the data jack, in accordance with the prior art the cores of at least two core pairs need to cross over one another, which can result in assignment errors or connection errors, in particular when in each case one data jack is intended to be connected to two opposite ends of a data cable, since the core pairs at the different ends of a data cable are each arranged in mirror-image fashion with respect to one another, when viewed in the viewing direction of the corresponding end of the data cable. Furthermore, crossing over the cores of different core pairs can impair the electrical transmission capacity. There is therefore a need for a connection system for connecting core pairs of a multi-pair data cable to connection pairs of a data jack which can be used to lay the core pairs of the data cable on the connection pairs of the data jack in a simplified and failsafe manner.